How to extrude an SVG on a cylinder but not have it solid
There is no need to convert the curve to mesh.
Start with the curve you imported.

Extrusion can be done in the curve's geometry section. To add some thickness use some bevel as well

Create a lattice object, make it so the resolution on the w axis is only one segment.

Use the lattice modifier on the curve, and have the lattice be the deforming object.

and then shrinkwrap the lattice to the cylinder.